Numerical integration for the Navier-Stokes equations in the regime of fully developed turbulence
Abstract
A numerical model based on the three-dimensional Navier-Stokes equations is presented for the case of an incompressible flow. Initial conditions defined by Taylor and Green are used, wherein behavior is modified as a function of the harmonics of the wave number. Six discrete symmetries are observed in the flow, three which are implicit in the concept of a cube of a side pi, where a vertical component appears in the presence of pressure. A pseudo spectral technique is employed with a second order time scheme, in order to take advantage of fast Fourier transformations in analyzing the nonlinear terms. An example is provided for a viscous flow, with Reynold numbers of 1600 and 3000. The presence of Taylor-Green vortices was found to cause overly large recovery in the latter case.
- Publication:
-
Academie des Sciences Paris Comptes Rendus Serie Sciences Mathematiques
- Pub Date:
- March 1982
- Bibcode:
- 1982CRASM.294..537B
- Keywords:
-
- Computational Fluid Dynamics;
- Incompressible Flow;
- Navier-Stokes Equation;
- Numerical Integration;
- Turbulent Flow;
- Viscous Flow;
- Energy Dissipation;
- Energy Spectra;
- Reynolds Number;
- Vortices;
- Fluid Mechanics and Heat Transfer